How do I denoise a simple grayscale image - matlab

Question

Here is the original image with better vision: we can see a lot of noise around the main skeleton, the circle thing, which I want to remove them, and do not affect the main skeleton. I'm not sure if it called noise
I'm doing it to deblurring a image, and this image is the motion blur kernel which identify the camera motion when the camera capture a image.
ps: this image is the kernel for one case, and what I need is a general method in here. thank you for your help
there is a paper in CVPR2014 named "Separable Kernel for Image Deblurring" which talk about this, I want to extract main skeleton of the image to make the kernel more robust, sorry for the explaination here as my English is not good
and here is the ture grayscale image:
I want it to be like this:
How can I do it using Matlab?
here are some other kernel images:

Answer 1

As #rayryeng well explained, median filtering is the best option to clean noise in the image, which I realized when I had studied about image restoration. However, in your case, what you need to do seems to me not cleaning noise in the image. You want to more likely eliminate the sparks in the image.
Simply I applied single thresholding to your noisy image to eliminate sparks.
Try this:
desIm = imread('http://i.stack.imgur.com/jyYUx.png'); % // Your expected (desired) image
nIm = imread('http://i.stack.imgur.com/pXO0p.png'); % // Your original image
nImgray = rgb2gray(nIm);
T = graythresh(nImgray)*255; % // Thereshold value
S = size(nImgray);
R = zeros(S) + 5; % // Your expected image bluish so I try to close it
G = zeros(S) + 3; % // Your expected image bluish so I try to close it
B = zeros(S) + 20; % // Your expected image bluish so I try to close it
logInd = nImgray > T; % // Logical index of pixel exclude spark component
R(logInd) = nImgray(logInd); % // Get original pixels without sparks
G(logInd) = nImgray(logInd); % // Get original pixels without sparks
B(logInd) = nImgray(logInd); % // Get original pixels without sparks
rgbImage = cat(3, R, G, B); % // Concatenating Red Green Blue channels
figure,
subplot(1, 3, 1)
imshow(nIm); title('Original Image');
subplot(1, 3, 2)
imshow(desIm); title('Desired Image');
subplot(1, 3, 3)
imshow(uint8(rgbImage)); title('Restoration Result');
What I got is:

Answer 2

The only thing I can see that is different between the two images is that there is some quantization noise / error around the perimeter of the object. This resembles salt and pepper noise and the best way to remove that noise is to use median filtering. The median filter basically analyzes local overlapping pixel neighbourhoods in your image, sorts the intensities and chooses the median value as the output for each pixel neighbourhood. Salt and pepper noise corrupts image pixels by randomly selecting pixels and setting their intensities to either black (pepper) or white (salt). By employing the median filter, sorting the intensities puts these noisy pixels at the lower and higher ends and by choosing the median, you would get the best intensity that could have possibly been there.
To do median filtering in MATLAB, use the medfilt2 function. This is assuming you have the Image Processing Toolbox installed. If you don't, then what I am proposing won't work. Assuming that you do have it, you would call it in the following way:
out = medfilt2(im, [M N]);
im would be the image loaded in imread and M and N are the rows and columns of the size of the pixel neighbourhood you want to analyze. By choosing a 7 x 7 pixel neighbourhood (i.e. M = N = 7), and reading your image directly from StackOverflow, this is the result I get:
Compare this image with your original one:
If you also look at your desired output, this more or less mimics what you want.
Also, the code I used was the following... only three lines!
im = rgb2gray(imread('http://i.stack.imgur.com/pXO0p.png'));
out = medfilt2(im, [7 7]);
imshow(out);
The first line I had to convert your image into grayscale because the original image was in fact RGB. I had to use rgb2gray to do that. The second line performs median filtering on your image with a 7 x 7 neighbourhood and the final line shows the image in a separate window with imshow.
Want to implement median filtering yourself?
If you want to get an idea of how to actually write a median filtering algorithm yourself, check out my recent post here. A question poser asked to implement the filtering mechanism without using medfilt2, and I provided an answer.
Matlab Median Filter Code
Hope this helps.
Good luck!